question_answer 21)

A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s. (a) How far will the cylinder go up the plane ? (b) How long will it take to return to the bottom ?  

Answer:

(a) Total initial kinetic energy of the cylinder,   Initial potential energy, Final kinetic energy,        Final potential energy,   where s is the distance travelled up the incline and h is the vertical height covered above the bottom. Gain in P.E. Loss in K.E. . (b) Using equation of motion for the motion up the incline, we get  or   Also,      or                          or              Total time taken in returning to the bottom .